Grand canonical Monte Carlo chemical potentials

FIG. 21 Dependence of the average density on the configurational chemical potential. The solid line denotes the grand canonical Monte Carlo data, the long dashed fine corresponds to the osmotic Monte Carlo results for ZL = 40, and the dotted line for ZL = 80. (From Ref. 172.)... 

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

The essential influence of surface roughening is also present in this model. Grand canonical Monte Carlo calculations were used to generate adatom populations at various temperatures up to Chemical potentials corresponding to those in the bulk LJ crystal were used, and these produced adatom densities that increased with temperature and roughly approximated the values observed in Ising model simulations below T. ... 

In the molecular simulation of adsorption in confined space such as pores of adsorbent, the most widely used and success l ensemble is the grand canonical Monte Carlo simulation. In this ensemble, we specify the chemical potential of the fluid,p, that the candidate pore is immersed in, the size of the pore, and the temperature. 

Cerius2 (MSI Inc.) was used throughout the simulations. Forcefield parameters obtained by Mellot et all. [3] are listed in Table 1. Ilie Grand Canonical Monte Carlo method (under constant chemical potential (p), volume (V), temperature (T)) was used to get the equilibrium amount adsorbed. 

In the grand-canonical Monte Carlo method, the system volume, temperature, and chemical potential are kept fixed, while the number of particles is allowed to fluctuate.There exist three types of trial move (1) displacement of a particle, (2) insertion of a particle, and (3) removal of a particle. These trial moves are generated at random with equal probability. The acceptance probability of the Metropolis method can be used for the trial moves of type (1). For the two other types, the acceptance probabilities are different. Regarding zeolites, an adsorption isotherm can be calculated with the grand-canonical Monte Carlo method by running a series of simulations at varying chemical potentials. 

In grand-canonical Monte Carlo the chemical potential is fixed whereas the number of particles fluctuates [21,22]. Here, besides the conventional trial displacements, moves are attempted that add or remove a particle and that are accepted with the following probabilities... 

The first method for simulating chemically reactive systems was proposed by Coker and Watts [11,12]. They presented a modified grand canonical Monte Carlo method wherein the total number of molecules is held fixed but the concentrations of the reacting species is allowed to vary. In their method a molecule is allowed to change species with a probability proportional to the exponential of the difference in chemical potentials between the two components. Thus, their method requires that the chemical potential differences be specified. Coker and Watts applied their method to the reaction... 

As we have aheady said, the grand canonical Monte Carlo provides a mean to determining the chemical potential, and hence, die free energy of the system. In other MC and MD calculations a numerical value for the free energy can always be obtained by means of an integration of thermodynamic relations along a path which links the state of interest to one for which the free energy is already known, for example, the dilute gas or the low-temperature solid. Such a procedure requires considerable computational effort, and it has alow numerical stability. Several methods have been proposed and tested. 

The grand canonical ensemble simulations model systems in which the chemical potential (/x), the volume and temperature are held fixed while the number of particles changes. The approach is very useful for simulating phase behavior which requires a constant chemical potential. Grand Canonical Monte Carlo simulation has been used to calculate sorption isotherms for a number of difierent microporous silicate systems. The simulations are used to model the equilibrium between zeolite and sorbate phases and, as such, it provides a natural way of simulating sorption isothermsl ... 

B. Jayaram and D. L. Beveridge,/. Phys. Chem., 95,2506 (1991). Grand Canonical Monte-Carlo Simulations on Aqueous Elutions of NaCI and NaDNA Excess Chemical Potentials and Sources of Nonideality in Electrolyte and Polyelectrolyte Solutions. 

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